This is the 8414th most frequent Japanese word.
悩み抜い
"悩み抜い" is not a standard Japanese word. If you meant "悩み抜く" (to struggle through worries), it means "to worry persistently or agonize over something."
悩み抜いて is used here to describe the thorough mental struggle or deliberation that took place before making a decision.
彼女は悩み抜いて重要な決断を下した。
She agonized intensely and made an important decision.
悩み抜いて in this sentence indicates enduring and extending thorough contemplation or worry for a prolonged period.
新しいプロジェクトに取り組む前に、彼は長い間悩み抜いていた。
Before tackling the new project, he had spent a long time deeply agonizing.
悩み抜いた末に implies the resolution or outcome following an exhaustive process of worrying or struggling with thoughts.